Forward Tim Duncan collected 19 points, seven rebounds and four assists for the Spurs, who took a 3-0 lead in the best-of-seven series that continues in Portland on Monday.
Five players scored in double figures for San Antonio, which again got great production from a bench that combined for 40 points, compared to six points from Portland's reserves.
The Spurs, behind 20 points on 9-for-12 shooting from Parker, held a 60-40 edge at halftime after San Antonio shot 56 percent from the field in the first half.
Portland made a run after the long break, outscoring San Antonio 17-4 in the first five minutes of the third quarter to draw within 64-57, but the Spurs steadied the ship and pulled away for the emphatic win.
Portland has led for only 33 seconds over the first three games of the series, such has been the dominance of the Spurs, who have won by a combined total of 56 points after being taken to seven games by Dallas in the first round of the playoffs.
San Antonio coach Gregg Popovich paid tribute to Parker, as well as his bench.
"Tony, he's been the engine for us and he started out really well tonight, he made shots and involved everybody else," Popovich told reporters. "He played great 'D' (defense) at the other end. He's really playing a complete game.
"We achieved home court advantage because the bench played so well all year long and allowed us to keep guys at 30 minutes or less the entire season. They've continued to be big for us this series."
Portland coach Terry Stotts acknowledged his team were guilty of leaving themselves too much to do after making poor starts.
"In some ways this is very similar to Games One and Two," he said. "We get down big in the first half and then play hard in the second half but the hole's too big.
"Against San Antonio, if you put your guard down they take advantage of it. They're good because they have a lot of options. Everybody's a threat.
"This is as well as I've seen them play all season. Game Seven against Dallas they came out of gate and they haven't stopped since then."
San Antonio, who finished the regular season with the best record in the league, last won the NBA championship in 2007.
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